Probably not. According to everything I've ever heard and every cannabis expert I can find online (ranging from Leafly.com to Marijuana: A History by Martin Booth) marijuana "kush" got its name from the Hindu Kush mountains. It was imported to the US from Afghanistan and got its name from the region.

The "Kush" in Hindu Kush is entirely unrelated to Hindi "kush" (ख़ुशी) [this may get confusing]. Where ख़ुशी means happiness, the name of the mountains comes from Persian "kushtan" (کشتن), which means "to kill." The Hindu Kush has been translated as the Hindu Slayer mountains, and supposedly takes its name from the number of Indian slaves who died in transit to Afghanistan and Iran.

Kush in the Hindi language actually also comes from Persian. Happiness in Sanskrit (the parent language of modern Hindi) was "Sukha" (सुख), but Hindi ultimately borrowed Persian "xushi" (خوشی), which also means happiness.

"Cannabis" itself is also an interesting word. It's incredibly ancient. Modern English ultimately gets it from ancient Greek, but linguists think it is much older. The word "hemp" is probably cognate through some sound changes in the Germanic languages in accordance with Grimm's Law (a linguistic principal). It seems to trace all the way back to the early proto-Indo-European root language. It's one of the words that helps support the hypothesis that Indo-European language originated in the Pontic-Caspian Steppe because cannabis (among many other shared Indo-European words) is native to that region.

It may also trace to ancient Semitic languages, like Akkadian, which called hemp "qunnapu" (𒋆𒄣𒌦𒈾𒁍). Alternatively, the borrowing could have gone the other way.

"Marijuana" is kind of a mystery word. It originated in Mexican Spanish, and linguists don't really know where it came from. It probably came from an indigenous American language, but which one is still debated.